96 Table of Propm'timal Logarithms, 
This table was printed in a Calcutta magazine in 1816, and^ 
as far as I know, has not appeared anywhere else ; nor have I 
been able to learn the name of the industrious computer, who 
certainly merits the thanks of the practical navigator and astro- 
nomer. Veoa. 
PropcnTional Logarithms to Twenty four Hours, 
This Table is useful for finding the proportional part of the 
daily variation of the Sun’s right ascension, and declination ; and 
of the equation of time, for any hour after noon. The numbers 
at the top to 24, are for hours ; and at the side minutes : or the 
first are minutes, and those at the side seconds. The top argu- 
ments are carried on to 30, as the daily variation of the equa- 
tion of time exceeds 30" on some days in December. 
The proportional logarithms in this Table, are found by sub- 
tracting the logarithms of the minutes in the several arguments, 
from the logarithm of the minutes in 24 hours, viz. 3.15836, 
So that the proportional logarithm of 24 becomes = 0. For 
tlie proportional logarithms above 24, the arithmetical com- 
plements of the logarithms of the arguments have been added 
to 3.15836, which renders it necessary to subtract 1 from the 
index of the result for every proportional logarithm taken from 
this part of the Table. 
RULE. 
To the proportional logarithm of the daily variation, add the 
proportional logarithm of the time from noon ; the sum is the 
proportional logarithm of the correction for that interval, to be 
added or subtracted according as the element employed is in- 
creasing or decreasing. 
When one or both the terms are small, arid, consequently, 
their proportional logarithms great, it is convenient, in order to 
prevent the answer falling near the beginning of the Table, 
where the differences are large, to take 1 or 2 from the index 
of the result, which will bring the answer out 10 or 100 times 
too great : this is readily done by the eye. 
The value of the terms of the answer is regulated by that of 
the arguments used ; and though on this point, at first an oc- 
casional ambiguity appears to occur, it is easily removed by a 
due consideration of the question. 
